Abstract
In previous chapters we have already discovered that traces give an incomplete picture of how processes behave, for example by failing to distinguish deterministic from nondeterministic behaviour and failing to capture deadlock properly. In this chapter we introduce the ideas of failures and divergences, which allow us to develop models that do capture these phenomena accurately. We see how these models allow to formulate and verify richer specifications on FDR. The phenomenon of divergence is described and we show one way to ensure it does not happen. We introduce lazy abstraction as a variant on hiding and show how it can be applied to capturing fault tolerance and computer security.
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- 1.
This is termed the stable failures model \(\mathcal {F}\).
- 2.
While the theory that allows us to build full CSP models without divergence strictness is complex, this does not mean that such models are hard to apply. In fact the difficulties only really appear for infinite-state processes rather than the finite-state ones that FDR can handle, and the model with failures and non-strict divergences could and should be implemented in FDR. The value given by this model to the token ring routing system with internal actions hidden is very natural: see Sect. 12.4.
- 3.
Though one needs to be careful with unboundedly nondeterministic ones.
- 4.
For details of the more advanced models now additionally supported, see Chaps. 11 and 12.
- 5.
There are a number of definitions of ‘security’ in the literature which would define such P′ to be secure for all P, even though if with \(P={\mathit {LEAK}}\/=hi?x\mathrel {\rightarrow }\mathit{lo}!x\mathrel {\rightarrow }\mathit{LEAK}\), for example, you can guarantee that if Hugh communicates anything with P′, then Lois gets to hear it.
References
Roscoe, A.W., Woodcock, J.C.P., Wulf, L.: Non-interference through determinism. J. Comput. Secur. 4(1), 27–54 (1996)
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© 2010 Springer-Verlag London Limited
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Roscoe, A.W. (2010). Beyond Traces. In: Understanding Concurrent Systems. Texts in Computer Science. Springer, London. https://doi.org/10.1007/978-1-84882-258-0_6
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DOI: https://doi.org/10.1007/978-1-84882-258-0_6
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